U.S. patent application number 16/406293 was filed with the patent office on 2020-07-30 for prediction control method and system for component contents in rare earth extraction process.
This patent application is currently assigned to East China Jiaotong University. The applicant listed for this patent is East China Jiaotong University. Invention is credited to Rongxiu Lu, Ying Wang, Gang Yang, Hui Yang, Jianyong Zhu.
Application Number | 20200239982 16/406293 |
Document ID | 20200239982 / US20200239982 |
Family ID | 1000004109393 |
Filed Date | 2020-07-30 |
Patent Application | download [pdf] |
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United States Patent
Application |
20200239982 |
Kind Code |
A1 |
Yang; Hui ; et al. |
July 30, 2020 |
Prediction Control Method And System For Component Contents In Rare
Earth Extraction Process
Abstract
The present invention discloses a prediction control method and
system for component contents in a rare earth extraction process.
The prediction control method includes: establishing an Elman
neural network model of a rare earth extraction process; obtaining
a predicted output value of the rare earth extraction process
through the Elman neural network model of the rare earth extraction
process; calculating an optimal set value through steady-state
optimization; dynamically predicting an extractant flow increment
and a detergent flow increment based on the predicted output value
and the optimal set value; and controlling component contents in
the rare earth extraction process according to the extractant flow
increment and the detergent flow increment. According to the
present invention, an optimal setting problem of a set point is
solved through steady-state optimization calculation, and then an
optimal control effect is achieved in combination with a dynamic
prediction control method, thereby achieving optimal setting
control over the component contents in the rare earth extraction
process, and ensuring the product quality of the rare earth
extraction process.
Inventors: |
Yang; Hui; (Nanchang City,
CN) ; Wang; Ying; (Nanchang City, CN) ; Lu;
Rongxiu; (Nanchang City, CN) ; Zhu; Jianyong;
(Nanchang City, CN) ; Yang; Gang; (Nanchang City,
CN) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
East China Jiaotong University |
Nanchang City |
|
CN |
|
|
Assignee: |
East China Jiaotong
University
Nanchang City
CN
|
Family ID: |
1000004109393 |
Appl. No.: |
16/406293 |
Filed: |
May 8, 2019 |
Current U.S.
Class: |
1/1 |
Current CPC
Class: |
G05B 13/027 20130101;
G05B 13/048 20130101; C22B 59/00 20130101; G06N 3/08 20130101; C22B
61/00 20130101; G06N 20/10 20190101 |
International
Class: |
C22B 59/00 20060101
C22B059/00; C22B 61/00 20060101 C22B061/00; G05B 13/04 20060101
G05B013/04; G05B 13/02 20060101 G05B013/02; G06N 3/08 20060101
G06N003/08; G06N 20/10 20060101 G06N020/10 |
Foreign Application Data
Date |
Code |
Application Number |
Jan 28, 2019 |
CN |
201910080799.2 |
Claims
1. A prediction control method for component contents in a rare
earth extraction process, wherein the prediction control method
comprises the following steps: establishing an Elman neural network
model of a rare earth extraction process; obtaining a predicted
output value of the rare earth extraction process through the Elman
neural network model of the rare earth extraction process;
calculating an optimal set value through steady-state optimization;
dynamically predicting an extractant flow increment and a detergent
flow increment based on the predicted output value and the optimal
set value; and controlling component contents in the rare earth
extraction process according to the extractant flow increment and
the detergent flow increment.
2. The prediction control method for component contents in a rare
earth extraction process according to claim 1, wherein the
establishing an Elman neural network model of a rare earth
extraction process specifically comprises: establishing an Elman
neural network model: { x ( k ) = f ( w 1 x c ( k ) + w 2 u ( k - 1
) + .theta. 1 ) x c ( k ) = x ( k - 1 ) y ( k ) = g ( w 3 x ( k ) +
.theta. 2 ) , ##EQU00019## wherein u(k-1) represents an input of
the Elman neural network model,
u(k-1)=[u.sub.1(k-1),u.sub.2(k-1)].sup.T; y(k) represents a
predicted output value, y(k)=[y.sub.1(k),y.sub.2(k)].sup.T,
y.sub.1(k) represents a predicted output value in an extraction
stage, and y.sub.2(k) represents a predicted output value in a
washing stage; x(k) represents an output of a hidden layer;
x.sub.c(k) represents an output of a structure layer; w.sup.1
represents a weight value connecting the structure layer and the
hidden layer; w.sup.2 represents a weight value connecting an input
layer and the hidden layer; w.sup.3 represents a weight value
connecting the hidden layer and an output layer; .theta..sub.1 and
.theta..sub.2 represent thresholds of the input layer and the
hidden layer respectively; f(*) represents a transfer function of a
hidden-layer neuron, and g(*) represents a transfer function of the
output layer; and training the Elman neural network model, and
obtaining the weight value connecting the structure layer and the
hidden layer, the weight value connecting the input layer and the
hidden layer, the weight value connecting the hidden layer and the
output layer, the threshold of the input layer, and the threshold
of the output layer, to obtain the Elman neural network model of
the rare earth extraction process.
3. The prediction control method for component contents in a rare
earth extraction process according to claim 1, wherein the
calculating an optimal set value through steady-state optimization
specifically comprises: establishing an economic performance
optimization target function of the component contents in the rare
earth extraction process: min M = c 1 u 1 + c 2 u 2 , s . t . { u
min .ltoreq. u .ltoreq. u max y min .ltoreq. y .ltoreq. y max
.DELTA. u min .ltoreq. .DELTA. u .ltoreq. .DELTA. u max ,
##EQU00020## wherein u.sub.1 and u.sub.2 represent an extractant
flow and a detergent flow respectively, u=[u.sub.1,u.sub.2].sup.T
represents an operation variable, c.sub.1 and c.sub.2 represent
costs of inputting a unit discharge of extractant and inputting a
unit discharge of detergent respectively, c=[c.sub.1,c.sub.2].sup.T
represents a cost variable, u.sub.max and u.sub.min are an
upper-bound constraint and a lower-bound constraint of the
operation variable u respectively, .DELTA.u represents an operation
variable increment, and .DELTA.u.sub.max and .DELTA.u.sub.min
represent an upper-bound constraint and a lower-bound constraint of
the operation variable increment .DELTA.u respectively; y.sub.1
represents component contents in an extraction stage, y.sub.1
represents component contents in a washing stage, and
y=[y.sub.1,y.sub.2].sup.T represents a controlled variable of the
extraction process; and y.sub.max and y.sub.min are an upper bound
and a lower bound meeting a control requirement which are obtained
through optimization calculation; and solving the economic
performance optimization target function, to obtain the optimal set
value.
4. The prediction control method for component contents in a rare
earth extraction process according to claim 1, wherein the
dynamically predicting an extractant flow increment and a detergent
flow increment based on the predicted output value and the optimal
set value specifically comprises: establishing a component content
deviation optimization target function based on the predicted
output value and the optimal set value: J = j = 1 P q ( j ) [ y ( k
+ j ) - w ( k + j ) ] 2 + j = 1 M r ( j ) [ .DELTA. u ( k + j - 1 )
] 2 , ##EQU00021## wherein P represents a maximum prediction
length, q(j) represents an error weighting coefficient that is j
steps ahead, y(k+j) represents a predicted output value that is j
steps ahead, and w(k+j) represents a tracked reference trajectory
that is j steps ahead;
w(k+j)=.alpha.w(k+j-1)+(1-.alpha.)y.sub.r(k+j), wherein .alpha. is
a softness factor, 0<.alpha.<1, w(k+j-1) represents a tracked
reference trajectory that is (j-1) steps ahead, and y.sub.r(k+j)
represents an optimal set value that is j steps ahead; M represents
a control length, r(j) represents a control weighting coefficient
that is j steps ahead, and .DELTA.u(k+j-1) represents a control
increment that is (j-1) steps ahead; and solving the component
content deviation optimization target function to obtain the
extractant flow increment and the detergent flow increment.
5. The prediction control method for component contents in a rare
earth extraction process according to claim 4, wherein the solving
the component content deviation optimization target function to
obtain the extractant flow increment and the detergent flow
increment specifically comprises: vectorizing the component content
deviation optimization target function to obtain a vector form of
the component content deviation optimization target function:
J=(Y-W).sup.TQ(Y-W)+R.DELTA.U.sup.T.DELTA.U, wherein W represents a
tracked reference trajectory vector, W=[w(k+1), w(k+2), . . . ,
w(k+P)].sup.T, Y represents a predicted output value vector,
.DELTA.U represents a control increment vector, Q represents a
target weighting matrix, and R represents a control weighting
matrix; substituting Y=G.DELTA.U+F into the vector form of the
component content deviation optimization target function to obtain
a solution function, J = ( G .DELTA. U + F - W ) T Q ( G .DELTA. U
+ F - W ) + R .DELTA. U T .DELTA. U = ( W - F ) T Q ( W - F ) - ( W
- F ) T QG .DELTA. U - .DELTA. U T G T Q ( W - F ) + .DELTA. U T G
T QG .DELTA. U + .DELTA. U T R .DELTA. U , ##EQU00022## wherein
F[f(k+1), f(k+2), . . . , f(k+P)].sup.T is a transfer function
value vector of a hidden-layer neuron of the Elman neural network
model of the rare earth extraction process, f(k+1), f(k+2), . . . ,
f(k+p) represent transfer function values of the hidden-layer
neuron of the Elman neural network model of the rare earth
extraction process which are 1 step ahead, 2 steps ahead, and P
steps ahead respectively, and G.di-elect
cons.R.sup.(2.times.M).times.(2.times.M) represents a control
matrix; and making .theta.J/.differential..DELTA.U=0, solving the
solution function to obtain a control increment optimal value
.DELTA.U*, wherein .DELTA.U*=(G.sup.TQG+RI).sup.-1QG.sup.T(W-F),
and obtaining the extractant flow increment and the detergent flow
increment, I being a unit matrix.
6. A prediction control system for component contents in a rare
earth extraction process, wherein the prediction control system
comprises: a model establishment module, configured to establish an
Elman neural network model of a rare earth extraction process; an
output value prediction module, configured to obtain a prediction
output value of the rare earth extraction process through the Elman
neural network model of the rare earth extraction process; an
optimal set value calculation module, configured to calculate an
optimal set value through steady-state optimization; a component
content increment prediction module, configured to dynamically
predict an extractant flow increment and a detergent flow increment
based on the predicted output value and the optimal set value; and
a process control module, configured to control component contents
in the rare earth extraction process according to the extractant
flow increment and the detergent flow increment.
7. The prediction control system for component contents in a rare
earth extraction process according to claim 6, wherein the model
establishment module specifically comprises: a model establishment
sub-module, configured to establish an Elman neural network model:
{ x ( k ) = f ( w 1 x c ( k ) + w 2 u ( k - 1 ) + .theta. 1 ) x c (
k ) = x ( k - 1 ) y ( k ) = g ( w 3 x ( k ) + .theta. 2 ) ,
##EQU00023## wherein u(k-1) represents an input of the Elman neural
network model, u(k-1)=[u.sub.1(k-1),u.sub.2(k-1)].sup.T; y(k)
represents a predicted output value,
y(k)=[y.sub.1(k),y.sub.2(k)].sup.T, y.sub.1(k) represents a
predicted output value in an extraction stage, and y.sub.2(k)
represents a predicted output value in a washing stage; x(k)
represents an output of a hidden layer; x.sub.c(k) represents an
output of a structure layer; w.sup.1 represents a weight value
connecting the structure layer and the hidden layer; w.sup.2
represents a weight value connecting an input layer and the hidden
layer; w.sup.3 represents a weight value connecting the hidden
layer and an output layer; .theta..sub.1 and .theta..sub.2
represent thresholds of the input layer and the hidden layer
respectively; f(*) represents a transfer function of a hidden-layer
neuron, and g(*) represents a transfer function of the output
layer; and a training sub-module, configured to train the Elman
neural network model, and obtain the weight value connecting the
structure layer and the hidden layer, the weight value connecting
the input layer and the hidden layer, the weight value connecting
the hidden layer and the output layer, the threshold of the input
layer, and the threshold of the output layer, to obtain the Elman
neural network model of the rare earth extraction process.
8. The prediction control system for component contents in a rare
earth extraction process according to claim 6, wherein the optimal
set value calculation module specifically comprises: an economic
performance optimization target function establishment sub-module,
configured to establish an economic performance optimization target
function of the component contents in the rare earth extraction
process: min M = c 1 u 1 + c 2 u 2 , s . t . { u min .ltoreq. u
.ltoreq. u max y min .ltoreq. y .ltoreq. y max .DELTA. u min
.ltoreq. .DELTA. u .ltoreq. .DELTA. u max , ##EQU00024## wherein
u.sub.1 and u.sub.2 represent an extractant flow and a detergent
flow respectively, u=[u.sub.1,u.sub.2].sup.T represents an
operation variable, c.sub.1 and c.sub.2 represent costs of
inputting a unit discharge of extractant and inputting a unit
discharge of detergent respectively, c=[c.sub.1,c.sub.2].sup.T
represents a cost variable, u.sub.max and u.sub.min are an
upper-bound constraint and a lower-bound constraint of the
operation variable u respectively, .DELTA.u represents an operation
variable increment, and .DELTA.u.sub.max and .DELTA.u.sub.min
represent an upper-bound constraint and a lower-bound constraint of
the operation variable increment .DELTA.u respectively; y.sub.1
represents component contents in an extraction stage, y.sub.1
represents component contents in a washing stage, and
y=[y.sub.1,y.sub.2].sup.T represents a controlled variable of the
extraction process; and y.sub.max and y.sub.min are an upper bound
and a lower bound meeting a control requirement which are obtained
through optimization calculation; and an economic performance
optimization target function solving sub-module, configured to
solve the economic performance optimization target function, to
obtain the optimal set value.
9. The prediction control system for component contents in a rare
earth extraction process according to claim 6, wherein the
component content increment prediction module specifically
comprises: a component content deviation optimization target
function establishment sub-module, configured to establish a
component content deviation optimization target function based on
the predicted output value and the optimal set value: J = j = 1 P q
( j ) [ y ( k + j ) - w ( k + j ) ] 2 + j = 1 M r ( j ) [ .DELTA. u
( k + j - 1 ) ] 2 , ##EQU00025## wherein P represents a maximum
prediction length, q(j) represents an error weighting coefficient
that is j steps ahead, y(k+j) represents a predicted output value
that is j steps ahead, and w(k+j) represents a tracked reference
trajectory that is j steps ahead;
w(k+j)=.alpha.w(k+j-1)+(1-.alpha.)y.sub.r(k+j), wherein .alpha. is
a softness factor, 0<.alpha.<1; w(k+j-1) represents a tracked
reference trajectory that is (j-1) steps ahead, and y.sub.r(k+j)
represents an optimal set value that is j steps ahead; M represents
a control length, r(j) represents a control weighting coefficient
that is j steps ahead, and .DELTA.u(k+j-1) represents a control
increment that is (j-1) steps ahead; and a component content
deviation optimization target function solving sub-module,
configured to solve the component content deviation optimization
target function to obtain the extractant flow increment and the
detergent flow increment.
10. The prediction control system for component contents in a rare
earth extraction process according to claim 6, wherein the
component content deviation optimization target function solving
sub-module specifically comprises: a function vectorization unit,
configured to vectorize the component content deviation
optimization target function to obtain a vector form of the
component content deviation optimization target function:
J=(Y-W).sup.TQ(Y-W)+R.DELTA.U.sup.T.DELTA.U, wherein W represents a
tracked reference trajectory vector, W=[w(k+1), w(k+2), . . . ,
w(k+P)].sup.T, Y represents a predicted output value vector,
.DELTA.U represents a control increment vector, Q represents a
target weighting matrix, and R represents a control weighting
matrix; a solution function obtaining unit, configured to
substitute Y=G.DELTA.U+F into the vector form of the component
content deviation optimization target function to obtain a solution
function, J = ( G .DELTA. U + F - W ) T Q ( G .DELTA. U + F - W ) +
R .DELTA. U T .DELTA. U = ( W - F ) T Q ( W - F ) - ( W - F ) T QG
.DELTA. U - .DELTA. U T G T Q ( W - F ) + .DELTA. U T G T QG
.DELTA. U + .DELTA. U T R .DELTA. U , ##EQU00026## wherein
F[f(k+1), f(k+2), . . . , f(k+P)].sup.T is a transfer function
value vector of a hidden-layer neuron of the Elman neural network
model of the rare earth extraction process, f(k+1), f(k+2), . . . ,
f(k+P) represent transfer function values of the hidden-layer
neuron of the Elman neural network model of the rare earth
extraction process which are 1 step ahead, 2 steps ahead, and P
steps ahead respectively, and G.di-elect
cons.R.sup.(2.times.M).times.(2.times.M) represents a control
matrix; and a solving unit, configured to make
.differential.J/.differential..DELTA.U=0, solve the solution
function to obtain a control increment optimal value .DELTA.U*,
wherein .DELTA.U*=(G.sup.TQG+RI).sup.-1QG.sup.T(W-F), and obtain
the extractant flow increment and the detergent flow increment, I
being a unit matrix.
Description
[0001] This application claims priority to Chinese application
number 201910080799.2, filed Jan. 28, 2019, with a title of
PREDICTION CONTROL METHOD AND SYSTEM FOR COMPONENT CONTENTS IN RARE
EARTH EXTRACTION PROCESS. The above-mentioned patent application is
incorporated herein by reference in its entirety.
TECHNICAL FIELD
[0002] The present invention relates to the field of process
control, and in particular, to a prediction control method and
system for component contents in a rare earth extraction
process.
BACKGROUND
[0003] With excellent physical, chemical, and electrical
properties, rare earth elements are widely applied in the
conventional industrial field, military field, and high-tech field,
and promote the technical progress of the related industries. In
the rare earth industry in China, a single high-purity rare earth
element is generally obtained using a solvent extraction method.
However, for a multi-variable system with a characteristic of
extremely complex operating condition changes in the rare earth
extraction process industry, the extraction and separation of the
rare earth element is a nonlinear, strong-coupling, severely lagged
complex industrial process. It is impossible to describe the
process by using a simple mechanism model, and it is also difficult
to design a high-efficient controller to control the process.
Currently, the rare earth extraction and separation industrial
process has a relatively low degree of automation. On-site online
detection has not been implemented yet. The extraction process
still needs to be controlled by seasoned operating personnel based
on their own experience. Through analysis on the rare earth
extraction industrial process, an important index for measuring the
quality of products at outlets of both ends of the process is
obtained, that is, the distribution of component contents in an
extraction tank. Therefore, the study on how to ensure that the
component contents at monitoring points at both ends of the rare
earth element extraction and separation process reach optimal set
values is of great significance for guaranteeing the improvement in
the product quality.
[0004] In the rare earth extraction process, modeling manners can
be generally classified into two types, that is, static modeling
and dynamic modeling. Establishment of a static model is mainly in
accordance with a cascade extraction equilibrium theory, and
dynamic characteristics in the extraction process are not taken
into account in the static model established in this manner. In the
existing technology, a bilinear model for the rare earth extraction
process is established by means of segmented aggregation modeling
in accordance with the principle of rare earth material
equilibrium. However, an inter-stage interaction mode of the
extraction tank is not taken into consideration, and the model
still has a large error.
[0005] If the rare earth element extraction mainly employs a
cascade extraction and separation technique, the rare earth
extraction process is a multi-input multi-output nonlinear process
that is particularly complex, and is affected by many factors. In
order to better optimize and control the rare earth extraction
process, a more accurate description model for the rare earth
extraction process needs to be established.
[0006] With the development of the industrial process technology,
the efficiency and stability of the rare earth industrial process
production as well as the purity of the rare earth product also
needs to meet increasingly higher requirements. Therefore, the
control technology related to component contents in the rare earth
extraction process is also developed to a certain degree.
Conventional control technologies include technologies based on a
PID control algorithm, and based on rare earth extraction process
control algorithms such as fuzzy control, an expert system, and
adaptive robust control. In the control technology based on the PID
control algorithm, during control over feeding flow rates of the
rare earth, influence of each flow rate on monitoring-stage
component content set values is ignored, thus failing to achieve an
expected effect. Based on the rare earth extraction process control
algorithms such as fuzzy control and the expert system, the input
of each stage is made fuzzy, and at the same time, the influence of
each flow rate on the monitoring-stage component content set values
is taken into consideration, thus improving the control effect.
However, the fuzzy control and expert system control are
implemented by simulating actual experience of experts, and when an
operating condition of an extraction site changes or is disturbed,
the control strategy cannot adjust parameters online in time.
Although the adaptive robust control method can take system
stability into consideration globally, it cannot measure dynamic
performance of the extraction process. As can be seen, none of the
existing control algorithms can meet an optimal control
standard.
SUMMARY
[0007] An objective of the present invention is to provide a
prediction control method and system for component contents in a
rare earth extraction process, so as to overcome the defects of the
existing control algorithms and meet an optimal control
standard.
[0008] To achieve the above objective, the present invention
provides the following solutions.
[0009] A prediction control method for component contents in a rare
earth extraction process includes the following steps:
[0010] establishing an Elman neural network model of a rare earth
extraction process;
[0011] obtaining a predicted output value of the rare earth
extraction process through the Elman neural network model of the
rare earth extraction process;
[0012] calculating an optimal set value through steady-state
optimization;
[0013] dynamically predicting an extractant flow increment and a
detergent flow increment based on the predicted output value and
the optimal set value; and
[0014] controlling component contents in the rare earth extraction
process according to the extractant flow increment and the
detergent flow increment.
[0015] Optionally, the establishing an Elman neural network model
of a rare earth extraction process specifically includes:
[0016] establishing an Elman neural network model:
{ x ( k ) = f ( w 1 x c ( k ) + w 2 u ( k - 1 ) + .theta. 1 ) x c (
k ) = x ( k - 1 ) y ( k ) = g ( w 3 x ( k ) + .theta. 2 ) ,
##EQU00001##
where u(k-1) represents an input of the Elman neural network model,
u(k-1)=[u.sub.1(k-1), u.sub.2(k-1)].sup.T; y(k) represents a
predicted output value, y(k)=[y.sub.1(k),y.sub.2(k)].sup.T,
y.sub.1(k) represents a predicted output value in an extraction
stage, and y.sub.2(k) represents a predicted output value in a
washing stage; x(k) represents an output of a hidden layer;
x.sub.c(k) represents an output of a structure layer; w.sup.1
represents a weight value connecting the structure layer and the
hidden layer; w.sup.2 represents a weight value connecting an input
layer and the hidden layer; w.sup.3 represents a weight value
connecting the hidden layer and an output layer; .theta..sub.1 and
.theta..sub.2 represent thresholds of the input layer and the
hidden layer respectively; f(*) represents a transfer function of a
hidden-layer neuron, and g(*) represents a transfer function of the
output layer; and
[0017] training the Elman neural network model, and obtaining the
weight value connecting the structure layer and the hidden layer,
the weight value connecting the input layer and the hidden layer,
the weight value connecting the hidden layer and the output layer,
the threshold of the input layer, and the threshold of the output
layer, to obtain the Elman neural network model of the rare earth
extraction process.
[0018] Optionally, the calculating an optimal set value through
steady-state optimization specifically includes:
[0019] establishing an economic performance optimization target
function of the component contents in the rare earth extraction
process:
min M = c 1 u 1 + c 2 u 2 , s . t . { u min .ltoreq. u .ltoreq. u
max y min .ltoreq. y .ltoreq. y max .DELTA. u m .ltoreq. .DELTA. u
.ltoreq. .DELTA. u max , ##EQU00002##
where u.sub.1 and u.sub.2 represent an extractant flow and a
detergent flow respectively, u=[u.sub.1,u.sub.2].sup.T represents
an operation variable, c.sub.1 and c.sub.2 represent costs of
inputting a unit discharge of extractant and inputting a unit
discharge of detergent respectively, c=[c.sub.1,c.sub.2].sup.T
represents a cost variable, u.sub.max and u.sub.min are an
upper-bound constraint and a lower-bound constraint of the
operation variable u respectively, .DELTA.u represents an operation
variable increment, and .DELTA.u.sub.max and .DELTA.u.sub.min
represent an upper-bound constraint and a lower-bound constraint of
the operation variable increment .DELTA.u respectively; y.sub.1
represents component contents in an extraction stage, y.sub.1
represents component contents in a washing stage, and
y=[y.sub.1,y.sub.2].sup.T represents a controlled variable of the
extraction process; and y.sub.max and y.sub.min are an upper bound
and a lower bound meeting a control requirement which are obtained
through optimization calculation; and
[0020] solving the economic performance optimization target
function, to obtain the optimal set value.
[0021] Optionally, the dynamically predicting an extractant flow
increment and a detergent flow increment based on the predicted
output value and the optimal set value specifically includes:
[0022] establishing a component content deviation optimization
target function based on the predicted output value and the optimal
set value:
J = j = 1 P q ( j ) [ y ( k + j ) - w ( k + j ) ] 2 + j = 1 M r ( j
) [ .DELTA. u ( k + j - 1 ) ] 2 , ##EQU00003##
where P represents a maximum prediction length, q(j) represents an
error weighting coefficient that is j steps ahead, y(k+j)
represents a predicted output value that is j steps ahead, and
w(k+j) represents a tracked reference trajectory that is j steps
ahead; w(k+k)=.alpha.w(k+j-1)+(1-.alpha.)y.sub.r(k+j), where
.alpha. is a softness factor, 0<.alpha.<1, w(k+j-1)
represents a tracked reference trajectory that is (j-1) steps
ahead, and y.sub.r(k+j) represents an optimal set value that is j
steps ahead; M represents a control length, r(j) represents a
control weighting coefficient that is j steps ahead, and
.DELTA.u(k+j-1) represents a control increment that is (j-1) steps
ahead; and
[0023] solving the component content deviation optimization target
function to obtain the extractant flow increment and the detergent
flow increment.
[0024] Optionally, the solving the component content deviation
optimization target function to obtain the extractant flow
increment and the detergent flow increment specifically
includes:
[0025] vectorizing the component content deviation optimization
target function to obtain a vector form of the component content
deviation optimization target function:
J=(Y-W).sup.TQ(Y-W)+R.DELTA.U.sup.T.DELTA.U, where W represents a
tracked reference trajectory vector, W=[w(k+1), w(k+2), . . . ,
w(k+P)].sup.T, Y represents a predicted output value vector,
.DELTA.U represents a control increment vector, Q represents a
target weighting matrix, and R represents a control weighting
matrix;
[0026] substituting Y=G.DELTA.U+F into the vector form of the
component content deviation optimization target function to obtain
a solution function,
J = ( G .DELTA. U + F - W ) T Q ( G .DELTA. U + F - W ) + R .DELTA.
U T .DELTA.U = ( W - F ) T Q ( W - F ) - ( W - F ) T Q G .DELTA. U
- .DELTA. U T G T Q ( W - F ) + .DELTA.U T G T Q G .DELTA. U +
.DELTA. U T R .DELTA. U , ##EQU00004##
where F=[f(k+1), f(k+2), . . . , f(k+P)].sup.T is a transfer
function value vector of a hidden-layer neuron of the Elman neural
network model of the rare earth extraction process, f(k+1), f(k+2),
. . . , f(k+P) represent transfer function values of the
hidden-layer neuron of the Elman neural network model of the rare
earth extraction process which are 1 step ahead, 2 steps ahead, and
P steps ahead respectively, and G.di-elect
cons.R.sup.(2.times.M).times.(2.times.M) represents a control
matrix; and
[0027] making .differential.J/.differential..DELTA.U=0, solving the
solution function to obtain a control increment optimal value
.DELTA.U*, where .DELTA.U*=(G.sup.TQG+RI).sup.-1QG.sup.T(W-F), and
obtaining the extractant flow increment and the detergent flow
increment, I being a unit matrix.
[0028] A prediction control system for component contents in a rare
earth extraction process includes:
[0029] a model establishment module, configured to establish an
Elman neural network model of a rare earth extraction process;
[0030] an output value prediction module, configured to obtain a
predicted output value of the rare earth extraction process through
the Elman neural network model of the rare earth extraction
process;
[0031] an optimal set value calculation module, configured to
calculate an optimal set value through steady-state
optimization;
[0032] a component content increment prediction module, configured
to dynamically predict an extractant flow increment and a detergent
flow increment based on the predicted output value and the optimal
set value; and
[0033] a process control module, configured to control component
contents in the rare earth extraction process according to the
extractant flow increment and the detergent flow increment.
[0034] Optionally, the model establishment module specifically
includes:
[0035] a model establishment sub-module, configured to establish an
Elman neural network model:
{ x ( k ) = f ( w 1 x c ( k ) + w 2 u ( k - 1 ) + .theta. 1 ) x c (
k ) = x ( k - 1 ) y ( k ) = g ( w 3 x ( k ) + .theta. 2 ) ,
##EQU00005##
where u(k-1) represents an input of the Elman neural network model,
u(k-1)=[u.sub.1(k-1),u.sub.2(k-1)].sup.T; y(k) represents a
predicted output value, y(k)=[y.sub.1(k),y.sub.2(k)].sup.T,
y.sub.1(k) represents a predicted output value in an extraction
stage, and y.sub.2(k) represents a predicted output value in a
washing stage; x(k) represents an output of a hidden layer;
x.sub.c(k) represents an output of a structure layer; w.sup.1
represents a weight value connecting the structure layer and the
hidden layer; w.sup.2 represents a weight value connecting an input
layer and the hidden layer; w.sup.3 represents a weight value
connecting the hidden layer and an output layer; .theta..sub.1 and
.theta..sub.2 represent thresholds of the input layer and the
hidden layer respectively; f(*) represents a transfer function of a
hidden-layer neuron, and g(*) represents a transfer function of the
output layer; and
[0036] a training sub-module, configured to train the Elman neural
network model, and obtain the weight value connecting the structure
layer and the hidden layer, the weight value connecting the input
layer and the hidden layer, the weight value connecting the hidden
layer and the output layer, the threshold of the input layer, and
the threshold of the output layer, to obtain the Elman neural
network model of the rare earth extraction process.
[0037] Optionally, the optimal set value calculation module
specifically includes:
[0038] an economic performance optimization target function
establishment sub-module, configured to establish an economic
performance optimization target function of the component contents
in the rare earth extraction process:
min M = c 1 u 1 + c 2 u 2 , s . t . { u min .ltoreq. u .ltoreq. u
max y min .ltoreq. y .ltoreq. y max .DELTA. u min .ltoreq. .DELTA.
u .ltoreq. .DELTA. u max , ##EQU00006##
where u.sub.1 and u.sub.2 represent an extractant flow and a
detergent flow respectively, u=[u.sub.1,u.sub.2].sup.T represents
an operation variable, c.sub.1 and c.sub.2 represent costs of
inputting a unit discharge of extractant and inputting a unit
discharge of detergent respectively, c=[c.sub.1,c.sub.2].sup.T
represents a cost variable, u.sub.max and u.sub.min are an
upper-bound constraint and a lower-bound constraint of the
operation variable u respectively, .DELTA.u represents an operation
variable increment, and .DELTA.u.sub.max and .DELTA.u.sub.min
represent an upper-bound constraint and a lower-bound constraint of
the operation variable increment .DELTA.u respectively; y.sub.1
represents component contents in an extraction stage, y.sub.1
represents component contents in a washing stage, and
y=[y.sub.1,y.sub.2].sup.T represents a controlled variable of the
extraction process; and y.sub.max and y.sub.min are an upper bound
and a lower bound meeting a control requirement which are obtained
through optimization calculation; and
[0039] an economic performance optimization target function solving
sub-module, configured to solve the economic performance
optimization target function, to obtain the optimal set value.
[0040] Optionally, the component content increment prediction
module specifically includes
[0041] a component content deviation optimization target function
establishment sub-module, configured to establish a component
content deviation optimization target function based on the
predicted output value and the optimal set value:
J = j = 1 P q ( j ) [ y ( k + j ) - w ( k + j ) ] 2 + j = 1 M r ( j
) [ .DELTA. u ( k + j - 1 ) ] 2 , ##EQU00007##
where P represents a maximum prediction length, q(j) represents an
error weighting coefficient that is j steps ahead, y(k+j)
represents a predicted output value that is j steps ahead, and
w(k+j) represents a tracked reference trajectory that is j steps
ahead; w(k+j)=.alpha.w(k+j-1)+(1-.alpha.)y.sub.r(k+j), where
.alpha. is a softness factor, 0<.alpha.<1; w(k+j-1)
represents a tracked reference trajectory that is (j-1) steps
ahead, and y.sub.r(k+j) represents an optimal set value that is j
steps ahead; M represents a control length, r(j) represents a
control weighting coefficient that is j steps ahead, and
.DELTA.u(k+j-1) represents a control increment that is (j-1) steps
ahead; and
[0042] a component content deviation optimization target function
solving sub-module, configured to solve the component content
deviation optimization target function to obtain the extractant
flow increment and the detergent flow increment.
[0043] Optionally, the component content deviation optimization
target function solving sub-module specifically includes:
[0044] a function vectorization unit, configured to vectorize the
component content deviation optimization target function to obtain
a vector form of the component content deviation optimization
target function: J=(Y-W).sup.TQ(Y-W)+R.DELTA.U.sup.T.DELTA.U, where
W represents a tracked reference trajectory vector, W=[w(k+1),
w(k+2), . . . , w(k+P)].sup.T, Y represents a predicted output
value vector, .DELTA.U represents a control increment vector, Q
represents a target weighting matrix, and R represents a control
weighting matrix;
[0045] a solution function obtaining unit, configured to substitute
Y=G.DELTA.U+F into the vector form of the component content
deviation optimization target function to obtain a solution
function,
J = ( G .DELTA. U + F - W ) T Q ( G .DELTA. U + F - W ) + R .DELTA.
U T .DELTA.U = ( W - F ) T Q ( W - F ) - ( W - F ) T Q G .DELTA. U
- .DELTA. U T G T Q ( W - F ) + .DELTA. U T G T Q G .DELTA. U +
.DELTA. U T R .DELTA. U , ##EQU00008##
where F[f(k+1), f(k+2), . . . , f(k+P)].sup.T is a transfer
function value vector of a hidden-layer neuron of the Elman neural
network model of the rare earth extraction process, f(k+1), f(k+2),
. . . , f(k+P) represent transfer function values of the
hidden-layer neuron of the Elman neural network model of the rare
earth extraction process which are 1 step ahead, 2 steps ahead, and
P steps ahead respectively, and G.di-elect
cons.R.sup.(2.times.M).times.(2.times.M) represents a control
matrix; and
[0046] a solving unit, configured to make
.differential.J/.differential..DELTA.U=0, solve the solution
function to obtain a control increment optimal value .DELTA.U*,
where .DELTA.U*=(G.sup.TQG+RI).sup.-1QG.sup.T(W-F), and obtain the
extractant flow increment and the detergent flow increment, I being
a unit matrix.
[0047] According to specific embodiments provided in the present
invention, the present invention discloses the following technical
effects:
[0048] The present invention discloses a prediction control method
and system for component contents in a rare earth extraction
process. According to the prediction control method provided in the
present invention, first of all, an Elman neural network model of a
rare earth extraction process is established, where a nonlinear
relationship of a CePr/Nd extraction and separation process is
described by using the Elman neural network model, and the Elman
neural network model includes a feedback link therein, which can
memorize status information of a previous moment and express a time
delay between an input quantity and an output quantity, thus being
capable of adapting to a time-variant characteristic; then, an
optimal set value is calculated through steady-state optimization;
besides, an extractant flow increment and a detergent flow
increment are predicted dynamically based on the predicted output
value and the optimal set value, and the component contents in the
rare earth extraction process are controlled according to the
extractant flow increment and the detergent flow increment. An
optimal setting problem of a set point is solved through
steady-state optimization calculation, and then an optimal control
effect is achieved in combination with a dynamic prediction control
method, thereby achieving optimal setting control over the
component contents in the rare earth extraction process, and
ensuring the product quality of the rare earth extraction
process.
BRIEF DESCRIPTION OF THE DRAWINGS
[0049] To describe the technical solutions in the embodiments of
the present invention or in the prior art more clearly, the
following briefly introduces the accompanying drawings required for
describing the embodiments. Apparently, the accompanying drawings
in the following description show merely some embodiments of the
present invention, and a person of ordinary skill in the art may
still derive other drawings from these accompanying drawings
without creative efforts.
[0050] FIG. 1 is a flowchart of a prediction control method for
component contents in a rare earth extraction process according to
the present invention;
[0051] FIG. 2 is a schematic diagram of a principle of a prediction
control method for component contents in a rare earth extraction
process according to the present invention;
[0052] FIG. 3 is a flowchart of a rare earth extraction process
according to the present invention;
[0053] FIG. 4 is a schematic diagram of an Elman neural network
model of a rare earth extraction process according to the present
invention;
[0054] FIG. 5 is an error curve graph of the Elman neural network
model of the rare earth extraction process;
[0055] FIG. 6 is a curve graph of a first predicted component
content;
[0056] FIG. 7 is a control quantity curve graph corresponding to
the curve graph of the first predicted component content;
[0057] FIG. 8 is a curve graph of a second predicted component
content;
[0058] FIG. 9 is a control quantity curve graph corresponding to
the curve graph of the second predicted component content; and
[0059] FIG. 10 is a structural composition block diagram of a
prediction control system for component contents in a rare earth
extraction process according to the present invention.
DETAILED DESCRIPTION
[0060] An objective of the present invention is to provide a
prediction control method and system for component contents in a
rare earth extraction process, so as to overcome the defects of the
existing control algorithms and meet an optimal control
standard.
[0061] To make the foregoing objectives, features, and advantages
of the present invention easier to understand, the following
describes the present invention in further detail with reference to
the accompanying drawings and specific embodiments.
Embodiment 1
[0062] Embodiment 1 of the present invention provides a prediction
control method for component contents in a rare earth extraction
process.
[0063] As shown in FIG. 1, the prediction control method includes
the following steps: step 101, establishing an Elman neural network
model of a rare earth extraction process; step 102, obtaining a
predicted output value of the rare earth extraction process through
the Elman neural network model of the rare earth extraction
process; step 103, calculating an optimal set value through
steady-state optimization; step 104, dynamically predicting an
extractant flow increment and a detergent flow increment based on
the predicted output value and the optimal set value; and step 105,
controlling component contents in the rare earth extraction process
according to the extractant flow increment and the detergent flow
increment.
[0064] Specifically, as shown in FIG. 2, y.sub.r(k) is an optimal
set value of a monitoring-stage component content after
steady-state target optimization calculation, and w(k) is a tracked
reference trajectory. An error e.sub.m(k) is obtained according to
a predicted output y.sub.m(k) of the Elman neural network model of
the rare earth extraction process and an on-site actual process
output y(k). Feedback correction is performed on parameters of the
Elman neural network model of the rare earth extraction process
according to a future predicted output y.sub.m(k+j) and an error at
the current moment, to obtain a corrected predicted output value
y.sub.p(k+j). Then, an error e(k) between the set value and the
corrected predicted output value is fed back to a dynamic
prediction controller, and an optimal control quantity u(k) of the
process is obtained through calculation, thereby controlling the
rare earth extraction process.
[0065] In the present invention, in view of the characteristics of
complexity and uncertainty of a rare earth extraction process, a
component content double-layer structured prediction controller
based on an Elman neural network model is designed. An optimal
setting problem of a set point is solved through steady-state
optimization calculation, and then an optimal control effect is
achieved in combination with a dynamic prediction control method,
thereby achieving optimal setting control over the component
contents in the rare earth extraction process, and ensuring the
product quality of the rare earth extraction process.
Embodiment 2
[0066] Embodiment 2 of the present invention provides a preferred
implementation manner of the prediction control method for
component contents in a rare earth extraction process. However, the
implementation of the present invention is not limited to the
implementation manner defined in Embodiment 2 of the present
invention.
[0067] The objective of the present invention is to establish a
high-precision Elman neural network model for a nonlinear system
with a complex operating condition characteristic of rare earth
extraction, and design a component content double-layer structured
prediction controller based on the model, so that an optimal
setting problem of set points of monitoring-stage component
contents is solved through steady-state optimization calculation,
and then a reference trajectory is tracked by using a dynamic
prediction control algorithm. The technical solution is as follows:
In view of the complex operating condition characteristics of
nonlinearity, strong coupling, and a severe lag of the rare earth
extraction process, an Elman neural network model description
method is proposed. With reference to dynamic process data of rare
earth elements CePr/Nd in different operation stages of the
extraction process, a rare earth extraction process identification
model is established by using an Elman neural network; it is
proposed to use a double-layer structured prediction control method
for component contents in a rare earth extraction process to
implement optimal setting control of the rare earth extraction
process.
[0068] Because the rare earth elements have similar chemical
properties and a small separation coefficient, the rare earth
cascade extraction and separation process shown in FIG. 3 is an
effective measure to obtain a single high-purity rare earth
element. In an industrial field, the value of a feed liquid flow is
usually determined by the actual yield of an industrial product,
and basically remains constant under the premise of guaranteed
benefits. Therefore, the rare earth extraction process can be
described as the following nonlinear functional relation:
{ y 1 ( k ) = f 1 [ y 1 ( k - 1 ) , u 1 ( k ) , u 2 ( k ) ] +
.zeta. 1 y 2 ( k ) = f 2 [ y 2 ( k - 1 ) , u 1 ( k ) , u 2 ( k ) ]
+ .zeta. 2 ##EQU00009##
In the formula, .zeta..sub.1, .zeta..sub.2 represent uncertain
factors in the extraction process respectively; monitoring-stage
component contents y.sub.1,y.sub.2 in an extraction stage and a
washing stage meet:
{ y 1 min .ltoreq. y 1 ( t ) .ltoreq. y 1 max y 2 min .ltoreq. y 2
( t ) .ltoreq. y 2 max ##EQU00010##
[0069] where y.sub.1min, y.sub.1max, y.sub.2min, y.sub.1max,
represent an upper bound and a lower bound of a component content
of a monitoring point respectively.
[0070] The study on the rare earth extraction process is usually
considered as a time sequence problem. The process is too complex,
and it is impossible to obtain relationships between component
contents and an extractant flow and between component contents and
a detergent flow through mechanism analysis. Therefore, the problem
is generally solved by establishing a neural network prediction
model. In the present invention, a nonlinear relationship of a
CePr/Nd extraction and separation process is described by using the
Elman neural network model, and the neural network includes a
feedback link therein, which can memorize status information of a
previous moment and express a time delay between an input quantity
and an output quantity, so that the system is capable of adapting
to a time-variant characteristic. Accordingly, the establishing an
Elman neural network model of a rare earth extraction process
specifically includes:
[0071] establishing an Elman neural network model:
{ x ( k ) = f ( w 1 x c ( k ) + w 2 u ( k - 1 ) + .theta. 1 ) x c (
k ) = x ( k - 1 ) y ( k ) = g ( w 3 x ( k ) + .theta. 2 ) ,
##EQU00011##
where u(k-1) represents an input of the Elman neural network model,
u(k-1)=[u.sub.1(k-1),u.sub.2(k-1)].sup.T; y(k) represents a
predicted output value, y(k)=[y.sub.1(k),y.sub.2(k)].sup.T,
y.sub.1(k) represents a predicted output value in an extraction
stage, and y.sub.2(k) represents a predicted output value in a
washing stage; x(k) represents an output of a hidden layer;
x.sub.c(k) represents an output of a structure layer; w.sup.1
represents a weight value connecting the structure layer and the
hidden layer; w.sup.2 represents a weight value connecting an input
layer and the hidden layer; w.sup.3 represents a weight value
connecting the hidden layer and an output layer; .theta..sub.1 and
.theta..sub.2 represent thresholds of the input layer and the
hidden layer respectively; f(*) represents a transfer function of a
hidden-layer neuron, and g(*) represents a transfer function of the
output layer; and
[0072] training the Elman neural network model, and obtaining the
weight value connecting the structure layer and the hidden layer,
the weight value connecting the input layer and the hidden layer,
the weight value connecting the hidden layer and the output layer,
the threshold of the input layer, and the threshold of the output
layer, to obtain the Elman neural network model of the rare earth
extraction process. The Elman neural network model of the rare
earth extraction process is as shown in FIG. 4.
[0073] It is proposed in the present invention that the optimal
setting control over the rare earth extraction process is
implemented by using a double-layer structured prediction control
method for component contents in a rare earth extraction process.
The double-layer structured prediction control includes two parts:
a steady-state optimization design layer on the left side gives an
optimal set value of a monitoring-stage component content in a rare
earth extraction tank, and a dynamic control layer on the right
side implements tracking and control over a target reference
trajectory of steady-state optimization by using a prediction
controller.
[0074] From the perspective of process control and optimization,
the rare earth extraction process is a multi-variable process with
complex characteristics such as strong coupling, a large lag, and
nonlinearity. Changes in the feed liquid flow, the extractant flow,
the detergent flow, and the like are major interference factors of
the stable and efficient operation of the rare earth extraction
process. In a control process of the practical rare earth
extraction industry, most control operations are completed by
experienced staff. Different personal experience and operation
habits as well as different control adjustment duration makes it
difficult to for parameters of the industrial process to achieve
relative stability, results in poor economic effectiveness of the
rare earth extraction process, and at the same time, also increases
the workload of the staff. Therefore, by taking economic
performance indexes and a control target requirement into
consideration comprehensively, the present invention introduces a
double-layer structured control system to improve the control and
optimization of the rare earth extraction process.
[0075] The feed liquid flow, the extractant flow, the detergent
flow, and other factors all have a certain influence on the
operating cost of the rare earth extraction process. In the
practical industrial production, the value of the feed liquid flow
is usually determined by the yield of the product, and basically
remains constant in the extraction process. Therefore, the
extractant flow and the detergent flow are major economic
performance indexes in the present invention.
[0076] Specifically, the calculating an optimal set value through
steady-state optimization specifically includes: establishing an
economic performance optimization target function of the component
contents in the rare earth extraction process:
min M = c 1 u 1 + c 2 u 2 , s . t . { u min .ltoreq. u .ltoreq. u
max y min .ltoreq. y .ltoreq. y max .DELTA. u min .ltoreq. .DELTA.
u .ltoreq. .DELTA. u max , ##EQU00012##
where u.sub.1 and u.sub.2 represent an extractant flow and a
detergent flow respectively, u=[u.sub.1,u.sub.2].sup.T represents
an operation variable, c.sub.1 and c.sub.2 represent costs of
inputting a unit discharge of extractant and inputting a unit
discharge of detergent respectively, c=[c.sub.1,c.sub.2].sup.T
represents a cost variable, u.sub.max and u.sub.min are an
upper-bound constraint and a lower-bound constraint of the
operation variable u respectively, .DELTA.u represents an operation
variable increment, and .DELTA.u.sub.max and .DELTA.u.sub.min
represent an upper-bound constraint and a lower-bound constraint of
the operation variable increment .DELTA.u respectively; y.sub.1
represents component contents in an extraction stage, y.sub.1
represents component contents in a washing stage, and
y=[y.sub.1,y.sub.2].sup.T represents a controlled variable of the
extraction process; and y.sub.max and y.sub.min are an upper bound
and a lower bound meeting a control requirement which are obtained
through optimization calculation; and solving the economic
performance optimization target function to obtain the optimal set
value.
[0077] The dynamically predicting an extractant flow increment and
a detergent flow increment based on the predicted output value and
the optimal set value specifically includes: in order to make a
monitoring-stage component content better track an expected set
value calculated through upper-layer steady-state optimization,
taking into consideration an influence of current-moment operation
variable u(k) on a future moment of the system in the target
function, and establishing a component content deviation
optimization target function based on the predicted output value
and the optimal set value:
J = j = 1 P q ( j ) [ y ( k + j ) - w ( k + j ) ] 2 + j = 1 M r ( j
) [ .DELTA. u ( k + j - 1 ) ] 2 , ##EQU00013##
where P represents a maximum prediction length, q(j) represents an
error weighting coefficient that is j steps ahead, y(k+j)
represents a predicted output value that is j steps ahead, and
w(k+j) represents a tracked reference trajectory that is j steps
ahead; w(k+j)=.alpha.w(k+j-1)+(1-.alpha.)y.sub.r(k+j), where
.alpha. is a softness factor, 0<.alpha.<1; w(k+j-1)
represents a tracked reference trajectory that is (j-1) steps
ahead, and y.sub.r(k+j) represents an optimal set value that is j
steps ahead; M represents a control length, r(j) represents a
control weighting coefficient that is j steps ahead, and
.DELTA.u(k+j-1) represents a control increment that is (j-1) steps
ahead; and solving the component content deviation optimization
target function to obtain the extractant flow increment and the
detergent flow increment.
[0078] The solving the component content deviation optimization
target function to obtain the extractant flow increment and the
detergent flow increment specifically includes: vectorizing the
component content deviation optimization target function to obtain
a vector form of the component content deviation optimization
target function: J=(Y-W).sup.TQ(Y-W)+R.DELTA.U.sup.T.DELTA.U where
W represents a tracked reference trajectory vector, W=[w(k+1),
w(k+2), . . . , w(k+P)].sup.T Y represents a predicted output value
vector, Y=[y(k+1), y(k+2), . . . , y(k+P)].sup.T; y(k+1), y(k+2),
and y(k+P) represent predicted output values that are 1 step ahead,
2 steps ahead, and P steps ahead respectively, .DELTA.U represents
a control increment vector, Q represents a target weighting matrix,
Q=block-diag{Q.sub.1, Q.sub.2, . . . , Q.sub.p},
Q.sub.i=diag{q.sub.i(1), q.sub.i(2), . . . q.sub.i(P)}, and R
represents a control weighting matrix, R block-diag{R.sub.1,
R.sub.2, . . . , R.sub.j=diag{r.sub.j(1), r.sub.j(2), . . . , };
substituting Y=G.DELTA.U+F into the vector form of the component
content deviation optimization target function to obtain a solution
function,
J = ( G .DELTA. U + F - W ) T Q ( G .DELTA. U + F - W ) + R .DELTA.
U T .DELTA. U = ( W - F ) T Q ( W - F ) - ( W - F ) T QG .DELTA. U
- .DELTA. U T G T Q ( W - F ) + .DELTA. U T G T QG .DELTA. U +
.DELTA. U T R .DELTA. U , ##EQU00014##
where F[f(k+1), f(k+2), . . . , f(k+P)].sup.T is a transfer
function value vector of a hidden-layer neuron of the Elman neural
network model of the rare earth extraction process, f(k+1), f(k+2),
. . . , f(k+P) represent transfer function values of the
hidden-layer neuron of the Elman neural network model of the rare
earth extraction process which are 1 step ahead, 2 steps ahead, and
P steps ahead respectively, and G.di-elect
cons.R.sup.(2.times.M).times.(2.times.M) represents a control
matrix; and
[0079] making .differential.J/.differential..DELTA.U=0, solving the
solution function to obtain a control increment optimal value
.DELTA.U*, where .DELTA.U*=(G.sup.TQG+RI).sup.-1QG.sup.T(W-F), and
obtaining the extractant flow increment and the detergent flow
increment, I being a unit matrix.
Embodiment 3
[0080] In order to verify the technical effect of the technical
solution of the present invention, Embodiment 3 of the present
invention provides a simulation verification method.
[0081] In the implementation of the present invention, a CePr/Nd
extraction and separation process is selected as a research object
of the experiment, and the description of a cascade extraction
process is shown in FIG. 3. Dynamic process data of the rare earth
elements CePr/Nd in different operation stages of the extraction
process is collected for modeling and simulation verification of
the control.
[0082] FIG. 5 is an error curve of a component content prediction
model. FIG. 5.a is a relative error curve of a model for component
contents in an extraction section; and FIG. 5.b is a relative error
curve of a model for component contents in a washing section. As
shown in FIG. 5, relative errors of training and testing of the
model for the CePr/Nd extraction and separation process are both
within .+-.2%, indicating that this model can simulate, with high
precision, nonlinear relationships between monitoring-stage
component contents at both ends and each controlled flow in the
rare earth extraction process.
[0083] Double-layer structured prediction control over the
component contents in the CePr/Nd extraction process is performed
by using the method according to the present invention, and FIG. 2
depicts the principle of the prediction control. According to the
requirements of the CePr/Nd extraction and separation process,
purity indexes of an easy-to-extract product and a
difficult-to-extract product at outlets of both ends of the
extraction tank should be kept at 0.9995 approximately; an optimal
extraction quantity is s=2.5661; the total number of stages of the
cascade extraction process is 60; the number of stages of the
extraction section and the number of stages of the washing section
are set to 26 and 34 respectively; the feed liquid flow u.sub.3 is
determined by the actual yield of the product, and is kept at 10
Lmin-1 herein. In the practical industry, to ensure the purity at a
water phase outlet and an organic phase outlet, the extraction
section and the washing section each should be provided with a
monitoring stage. The selection of the number of the sensitive
monitoring point stages, that is, the selection of the optimal set
value of the component content, has an influence on the adjustment
of the extractant flow and the detergent flow. To ensure the purity
at the outlets, it is set that control quantity constraints of the
rare earth extraction process are as follows:
11.7870.ltoreq.u.sub.1.ltoreq.18.1207,
5.7415.ltoreq.u.sub.2.ltoreq.9.7418; given constraint ranges of
controlled quantities are as follows:
0.9435.ltoreq.y.sub.1.ltoreq.0.9935,
0.8783.ltoreq.y.sub.2.ltoreq.0.9383; control quantity increment
constraints are [-0.05, 0.05].sup.T; and a cost coefficient of a
steady-state optimization layer is configured as follows:
c.sub.1=-2, c.sub.2=-1, where - represents benefits. With reference
to features of the CePr/Nd extraction process, economic
optimization is first performed in the steady-state optimization
layer to obtain an optimal output value and an optimal working
point, thereby providing a control target for a dynamic control
layer.
[0084] It can be learned from FIG. 6 to FIG. 9 that, the
double-layer structured prediction controller for the rare earth
extraction process can adjust the extractant and the detergent flow
in time, so that the monitoring-stage component content is
stabilized at the optimal set value, thus ensuring the quality of
product at outlets of both ends, and also meeting the requirements
for economy, high efficiency, and stability on the practical rare
earth extraction process.
Embodiment 4
[0085] Embodiment 4 of the present invention provides a prediction
control system for component contents in a rare earth extraction
process.
[0086] As shown in FIG. 10, the prediction control system includes:
a model establishment module 1001, configured to establish an Elman
neural network model of a rare earth extraction process; an output
value prediction module 1002, configured to obtain a predicted
output value of the rare earth extraction process through the Elman
neural network model of the rare earth extraction process; an
optimal set value calculation module 1003, configured to calculate
an optimal set value through steady-state optimization; a component
content increment prediction module 1004, configured to dynamically
predict an extractant flow increment and a detergent flow increment
based on the predicted output value and the optimal set value; and
a process control module 1005, configured to control component
contents in the rare earth extraction process according to the
extractant flow increment and the detergent flow increment.
Embodiment 5
[0087] Embodiment 5 of the present invention provides a preferred
implementation manner of a prediction control system for component
contents in a rare earth extraction process. However, the
implementation of the present invention is not limited to the
implementation manner defined in Embodiment 5 of the present
invention.
[0088] The model establishment module 1001 specifically includes: a
model establishment sub-module, configured to establish an Elman
neural network model:
{ x ( k ) = f ( w 1 x c ( k ) + w 2 u ( k - 1 ) + .theta. 1 ) x c (
k ) = x ( k - 1 ) y ( k ) = g ( w 3 x ( k ) + .theta. 2 ) ,
##EQU00015##
where u(k-1) represents an input of the Elman neural network model,
u(k-1)=[u.sub.1(k-1),u.sub.2(k-1)].sup.T; y(k) represents a
predicted output value, y(k)=[y.sub.1(k),y.sub.2(k)].sup.T,
y.sub.1(k) represents a predicted output value in an extraction
stage, and y.sub.2(k) represents a predicted output value in a
washing stage; x(k) represents an output of a hidden layer;
x.sub.c(k) represents an output of a structure layer; w.sup.1
represents a weight value connecting the structure layer and the
hidden layer; w.sup.2 represents a weight value connecting an input
layer and the hidden layer; w.sup.3 represents a weight value
connecting the hidden layer and an output layer; .theta..sub.1 and
.theta..sub.2 represent thresholds of the input layer and the
hidden layer respectively; f(*) represents a transfer function of a
hidden-layer neuron, and g(*) represents a transfer function of the
output layer; and a training sub-module, configured to train the
Elman neural network model, and obtain the weight value connecting
the structure layer and the hidden layer, the weight value
connecting the input layer and the hidden layer, the weight value
connecting the hidden layer and the output layer, the threshold of
the input layer, and the threshold of the output layer, to obtain
the Elman neural network model of the rare earth extraction
process.
[0089] The optimal set value calculation module 1003 specifically
includes: an economic performance optimization target function
establishment sub-module, configured to establish an economic
performance optimization target function of the component contents
in the rare earth extraction process:
min M = c 1 u 1 + c 2 u 2 , s . t . { u min .ltoreq. u .ltoreq. u
max y min .ltoreq. y .ltoreq. y max .DELTA. u min .ltoreq. .DELTA.
u .ltoreq. .DELTA. u max , ##EQU00016##
where u.sub.1 and u.sub.2 represent an extractant flow and a
detergent flow respectively, u=[u.sub.1,u.sub.2].sup.T represents
an operation variable, c.sub.1 and c.sub.2 represent costs of
inputting a unit discharge of extractant and inputting a unit
discharge of detergent respectively, c=[c.sub.1,c.sub.2].sup.T
represents a cost variable, u.sub.max and u.sub.min are an
upper-bound constraint and a lower-bound constraint of the
operation variable u respectively, .DELTA.u represents an operation
variable increment, and .DELTA.u.sub.max and .DELTA.u.sub.min
represent an upper-bound constraint and a lower-bound constraint of
the operation variable increment .DELTA.u respectively; y.sub.1
represents component contents in an extraction stage, y.sub.1
represents component contents in a washing stage, and
y=[y.sub.1,y.sub.2].sup.T represents a controlled variable of the
extraction process; and y.sub.max and y.sub.min are an upper bound
and a lower bound meeting a control requirement which are obtained
through optimization calculation; and an economic performance
optimization target function solving sub-module, configured to
solve the economic performance optimization target function, to
obtain the optimal set value.
[0090] The component content increment prediction module 1004
specifically includes: a component content deviation optimization
target function establishment sub-module, configured to establish a
component content deviation optimization target function based on
the predicted output value and the optimal set value:
J = j = 1 P q ( j ) [ y ( k + j ) - w ( k + j ) ] 2 + j = 1 M r ( j
) [ .DELTA. u ( k + j - 1 ) ] 2 , ##EQU00017##
where P represents a maximum prediction length, q(j) represents an
error weighting coefficient that is j steps ahead, y(k+j)
represents a predicted output value that is j steps ahead, and
w(k+j) represents a tracked reference trajectory that is j steps
ahead; w(k+j)=.alpha.w(k+j-1)+(1-.alpha.)y.sub.r(k+j), where a is a
softness factor, 0<.alpha.<1; w(k+j-1) represents a tracked
reference trajectory that is (j-1) steps ahead, and y.sub.r(k+j)
represents an optimal set value that is j steps ahead; M represents
a control length, r(j) represents a control weighting coefficient
that is j steps ahead, and .DELTA.u(k+j-1) represents a control
increment that is (j-1) steps ahead; and a component content
deviation optimization target function solving sub-module,
configured to solve the component content deviation optimization
target function to obtain the extractant flow increment and the
detergent flow increment.
[0091] The component content deviation optimization target function
solving sub-module specifically includes: a function vectorization
unit, configured to vectorize the component content deviation
optimization target function to obtain a vector form of the
component content deviation optimization target function:
J=(Y-W).sup.TQ(Y-W)+R.DELTA.U.sup.T.DELTA.U, where W represents a
tracked reference trajectory vector W=[w(k+1), w(k+2), . . . ,
w(k+P)].sup.T, Y represents a predicted output value vector
Y=[y(k+1), y(k+2), . . . , y(k+P)].sup.T; y(k+1), y(k+2), and
y(k+P) represent predicted output values that are 1 step ahead, 2
steps ahead, and P steps ahead respectively, .DELTA.U represents a
control increment vector, Q represents a target weighting matrix,
and R represents a control weighting matrix; a solution function
obtaining unit, configured to substitute Y=G.DELTA.U+F into the
vector form of the component content deviation optimization target
function to obtain a solution function,
J = ( G .DELTA. U + F - W ) T Q ( G .DELTA. U + F - W ) + R .DELTA.
U T .DELTA. U = ( W - F ) T Q ( W - F ) - ( W - F ) T QG .DELTA. U
- .DELTA. U T G T Q ( W - F ) + .DELTA. U T G T QG .DELTA. U +
.DELTA. U T R .DELTA. U , ##EQU00018##
where F=[f(k+1), f(k+2), . . . , f(k+P)].sup.T is a transfer
function value vector of a hidden-layer neuron of the Elman neural
network model of the rare earth extraction process, f(k+1), f(k+2),
. . . , .theta.(k+P) represent transfer function values of the
hidden-layer neuron of the Elman neural network model of the rare
earth extraction process which are 1 step ahead, 2 steps ahead, and
P steps ahead respectively, and G.di-elect
cons.R.sup.(2.times.M).times.(2.times.M) represents a control
matrix; and a solving unit, configured to make
.differential.J/.differential..DELTA.U=0, solve the solution
function to obtain a control increment optimal value .DELTA.U*,
where .DELTA.U*=(G.sup.TQG+RI).sup.-1QG.sup.T(W-F), and obtain the
extractant flow increment and the detergent flow increment, I being
a unit matrix.
[0092] Compared with the prior art, the present invention achieves
the following beneficial effects: Due to the characteristics of
strong coupling and nonlinearity of the rare earth extraction
process, a static model for components at outlets of both ends is
usually employed for the process design. However, the conventional
static model cannot implement online prediction and real-time
adjustment of the contents of rare earth element components at each
cascade stage in the rare earth extraction process, and a process
model cannot be constructed, thus affecting the subsequent control
effect of the contents of the rare earth elements. In the present
technical solution, sample data generated during operation of
different stages of the CePr/Nd extraction process is analyzed
first, and major parameters influencing the extraction process are
determined according to characteristics of the data and actual
requirements on site, to establish an Elman neural network model
and obtain a prediction result. A double-layer structured
prediction control method for component contents in a rare earth
extraction process is proposed. Economic performance in the
extraction process is fully considered. A controlled output
expected target value is calculated through a steady-state
optimization layer of the double-layer structured prediction
control, so as to replace a given value based on human experience,
thus implementing optimization of a set point. Then, an optimal
control quantity of the rare earth extraction process is obtained
through a dynamic prediction control layer of the design, and it is
ensured that the quality of product at both ends is optimized.
[0093] Each embodiment of the present specification is described in
a progressive manner, each embodiment focuses on the difference
from other embodiments, and the same and similar parts between the
embodiments may refer to each other. For a system disclosed in the
embodiments, since it corresponds to the method disclosed in the
embodiments, the description is relatively simple, and reference
can be made to the method description.
[0094] The principles and implementations of the present invention
have been described with reference to specific examples. The
description of the above embodiments is only for facilitating
understanding of the method and the core idea of the present
invention, and the described embodiments are only a part of the
embodiments of the present invention. All other embodiments
obtained by a person of ordinary skill in the art based on the
embodiments of the present invention without departing from the
inventive scope are the scope of the present invention.
* * * * *